{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
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       " $('div.input').show();\n",
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       "$( document ).ready(code_toggle);\n",
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       "<form action=\"javascript:code_toggle()\"><input type=\"submit\" value=\"Click here to toggle on/off the raw code.\"></form>"
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    "from IPython.display import HTML\n",
    "\n",
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    "<form action=\"javascript:code_toggle()\"><input type=\"submit\" value=\"Click here to toggle on/off the raw code.\"></form>''')"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Teachers Prediction:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Predict bad teacher:\n",
    "This part of the jupyter's notebook computes different models to predict if a teacher performed bad (least 30 percentile) in the portfolio test based on information we have about their performance in PAA/PSU and GPA."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import os\n",
    "import seaborn as sns; sns.set(color_codes=True)\n",
    "%matplotlib inline\n",
    "from matplotlib import pyplot\n",
    "import matplotlib.pyplot as plt\n",
    "import plotly.plotly as py\n",
    "from scipy import stats\n",
    "from sklearn import datasets, linear_model, preprocessing\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.model_selection import train_test_split, cross_val_score\n",
    "from sklearn import tree, svm\n",
    "from sklearn.metrics import accuracy_score, roc_auc_score\n",
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let's open the information available to run the models:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>periodo</th>\n",
       "      <th>ciclo</th>\n",
       "      <th>subsector</th>\n",
       "      <th>pf_pje</th>\n",
       "      <th>instr_pje</th>\n",
       "      <th>esc_r</th>\n",
       "      <th>Te_EvLevel</th>\n",
       "      <th>proceso</th>\n",
       "      <th>pref</th>\n",
       "      <th>cod</th>\n",
       "      <th>...</th>\n",
       "      <th>DeltaAvePrivado2</th>\n",
       "      <th>Duration</th>\n",
       "      <th>Duration2</th>\n",
       "      <th>DeltaDuration</th>\n",
       "      <th>DeltaDuration2</th>\n",
       "      <th>Type1</th>\n",
       "      <th>Type2</th>\n",
       "      <th>Type3</th>\n",
       "      <th>Type4</th>\n",
       "      <th>_merge</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2006</td>\n",
       "      <td>2do Ciclo</td>\n",
       "      <td>Matemtica</td>\n",
       "      <td>2.27</td>\n",
       "      <td>2.66</td>\n",
       "      <td>Competente</td>\n",
       "      <td>2</td>\n",
       "      <td>1977</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3537</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.014692</td>\n",
       "      <td>6.0</td>\n",
       "      <td>36.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2006</td>\n",
       "      <td>2do Ciclo</td>\n",
       "      <td>Matemtica</td>\n",
       "      <td>2.27</td>\n",
       "      <td>2.66</td>\n",
       "      <td>Competente</td>\n",
       "      <td>2</td>\n",
       "      <td>1978</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3303</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5.0</td>\n",
       "      <td>25.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2 rows × 159 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   periodo      ciclo  subsector  pf_pje  instr_pje       esc_r  Te_EvLevel  \\\n",
       "0     2006  2do Ciclo  Matemtica    2.27       2.66  Competente           2   \n",
       "1     2006  2do Ciclo  Matemtica    2.27       2.66  Competente           2   \n",
       "\n",
       "   proceso  pref   cod   ...    DeltaAvePrivado2  Duration  Duration2  \\\n",
       "0     1977   1.0  3537   ...           -0.014692       6.0       36.0   \n",
       "1     1978   3.0  3303   ...                 NaN       5.0       25.0   \n",
       "\n",
       "   DeltaDuration  DeltaDuration2  Type1  Type2  Type3  Type4  _merge  \n",
       "0            1.0            11.0      0      1      0      0       3  \n",
       "1            NaN             NaN      0      1      0      0       3  \n",
       "\n",
       "[2 rows x 159 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_path = os.getcwd() + '/data/PAA-evdoc.csv'\n",
    "df = None\n",
    "#with open(df_path, encoding=\"utf-16\") as f:\n",
    "with open(df_path, encoding=\"utf8\", errors='ignore') as f:\n",
    "    df = pd.read_csv(f)\n",
    "\n",
    "df.head(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Quick df clean:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Quick df clean:\n",
    "scores = ['paa_verbal', 'paa_matematica', 'nem', 'gpa', 'pce_hria_y_geografia', 'pce_biologia', 'pce_cs_sociales', 'pce_fisica', 'pce_matematica', 'pce_quimica']\n",
    "cat = ['region', 'male']\n",
    "df_s = df[scores].copy()\n",
    "\n",
    "bygroup = 0\n",
    "if bygroup == 1:\n",
    "    df_s['periodo'] = df['periodo']\n",
    "    df_s = df_s.groupby('periodo').transform(lambda x: (x - x.mean()) / x.std())\n",
    "else:\n",
    "    df_s = (df[scores] - df[scores].mean())/df[scores].std()\n",
    "df_s['Average'] = (df['paa_verbal'] + df['paa_matematica'])/2\n",
    "\n",
    "df_c = df[cat].copy()\n",
    "\n",
    "df_s['took_hist'] = (df.pce_hria_y_geografia == 0)\n",
    "df_s['took_bio'] = (df.pce_biologia == 0)\n",
    "df_s['took_soc'] = (df.pce_cs_sociales == 0)\n",
    "df_s['took_fis'] = (df.pce_fisica == 0)\n",
    "df_s['took_mat'] = (df.pce_matematica == 0)\n",
    "df_s['took_qui'] = (df.pce_quimica == 0)\n",
    "\n",
    "y = df['pf_pje']\n",
    "\n",
    "df = pd.concat([df_s, df_c, y], axis=1)\n",
    "\n",
    "df = df.dropna()\n",
    "df.region = df.region.astype(int)\n",
    "df.male = df.male.astype(int)\n",
    "\n",
    "#Divide the sample distribution in 10 types:\n",
    "df['xtile'] = pd.qcut(df.pf_pje, 10, labels = ['percentil: '+str(i) for i in range(10)])\n",
    "df['worst'] = (df['xtile'] == 'percentil: 0' ) | (df['xtile'] == 'percentil: 1') | (df['xtile'] == 'percentil: 2')\n",
    "\n",
    "df.columns = ['paaverbal' if x=='paa_verbal' else 'paamat' if x =='paa_matematica' else x for x in df.columns] #Change colname\n",
    "\n",
    "x_variables = [x if (x!='pf_pje' and x!='xtile' and x!='worst' and x!='region9') else \"AAA\" for x in list(df)]\n",
    "x_variables = sorted(list(set(x_variables)))\n",
    "del x_variables[0]\n",
    "\n",
    "X_transformed = df[x_variables].dropna().drop(columns = ['region',\n",
    "'pce_biologia', 'pce_cs_sociales', 'pce_fisica', 'pce_hria_y_geografia', 'pce_matematica', 'pce_quimica'])\n",
    "#'took_bio', 'took_fis', 'took_hist', 'took_mat', 'took_qui', 'took_soc', 'paamat', 'paaverbal'\n",
    "\n",
    "X_transformed['paa_avg'] = (X_transformed.Average - X_transformed.Average.mean())/X_transformed.Average.std()\n",
    "Y = df['worst']      #Here we have the indicator of bad teacher\n",
    "y_pf = (df['pf_pje'] - df['pf_pje'].mean())/df['pf_pje'].std()  #Here the pf_pje\n",
    "X_transformed = X_transformed.drop(columns = ['Average', 'paa_avg', 'gpa'])\n",
    "\n",
    "X_train_transformed, X_test_transformed, y_train, y_test = train_test_split(X_transformed, Y, test_size=0.15)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.1. Likelihood vs teacher performance scatterplot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define a function which inserts the predictions (predict) and the likelihood (predict_proba) in the main dataframe. One can easily change the model introducing the name of the predictive model in the args."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def gen_predictions(Classifier, X_train, X_test, y_train):\n",
    "    from sklearn import tree, svm\n",
    "    SVC = svm.SVC\n",
    "    if Classifier == SVC:\n",
    "        clf = Classifier(C=1, probability=True)\n",
    "    else:\n",
    "        clf = Classifier()\n",
    "    clf = clf.fit(X_train, y_train)\n",
    "\n",
    "    y_test_hat = clf.predict_proba(X_test)[:,1]  #Prob of bad Teacher\n",
    "    y_test_predict = clf.predict(X_test)  #Prob of bad Teacher\n",
    "\n",
    "    ndf = y_test_hat.shape[0]\n",
    "    df_ml_test = X_test.copy()\n",
    "    df_ml_test['y_test_hat'] = y_test_hat\n",
    "    df_ml_test = df_ml_test.sort_values(by = ['y_test_hat'])\n",
    "\n",
    "    return df_ml_test, clf.predict_proba(X_test), y_test_predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df_rf_test , y_test_hat, y_test_predict = gen_predictions(RandomForestClassifier, X_train_transformed, X_test_transformed, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overall Accuracy: 0.90 \n",
      "Type 1 error: 0.24 \n",
      "Type 2 error:  0.09\n"
     ]
    }
   ],
   "source": [
    "accuracy = np.mean(y_test_predict == y_test)\n",
    "type1_error = 1 - np.mean(y_test[y_test==1] == y_test_predict[y_test==1]) #Type 1 error: Probabilidad de predecir que no es malo cuando si lo es\n",
    "type2_error = 1 - np.mean(y_test[y_test_predict == 1] == y_test_predict[y_test_predict == 1]) #probabilidad de predecir que profesor es malo cuando en realidad es bueno (Error tipo 2)\n",
    "\n",
    "print(\"Overall Accuracy: %.2f \\nType 1 error: %.2f \\nType 2 error:  %.2f\" % (accuracy, type1_error, type2_error))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot Results of the Model. In this case we are using Random forest Estimation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Graph 1.1: Likelihood vs PAA Math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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tj+8D31/A/ePATcD5+JfDnhCRu1X1xdBhDwJ3B30u24DvACeUeV9Tpl1nH8uu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\nGJ/M8tjzByL3/fTFt7l472B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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a7d88da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(df_rf_test.paamat, df_rf_test.y_test_hat, x_bins = 15)\n",
    "plt.ylabel(r'$\\^Yprob$')\n",
    "plt.xlabel('PAA Math')\n",
    "plt.show()\n",
    "#plt.savefig(r'C:\\\\Users\\\\Franco\\\\GitHub\\\\teacher-predictions\\\\output\\\\Pr_vs_paa_mat.pdf', bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Graph 1.2: Likelihood vs PAA Verbal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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RlpIAcvVFW4iv8OK7sAp/o67n/52Xry0vTpvK5MnV2AihmlTCYeMc61ozf2jm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\n4dDQWEU5aiPVKz1hj1PPzyP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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a7130470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(df_rf_test.paaverbal, df_rf_test.y_test_hat, x_bins = 15)\n",
    "plt.ylabel(r'$\\^Yprob$')\n",
    "plt.xlabel('PAA Verbal')\n",
    "plt.show()\n",
    "#plt.savefig(r'C:\\\\Users\\\\Franco\\\\GitHub\\\\teacher-predictions\\\\output\\\\Pr_vs_paa_verbal.pdf', bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Graph 1.3: Likelihood vs PAA Average"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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qZ4Z6cgE3G2hmrE45lVsbxgmQm4PMy8VMN5mthnEuSwkgI8AeEblDVff5ifSF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\nYgHEGGNMWf5/PiHj4dZ8WPQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a6fbb240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_rf_test['paa_avg'] = (df_rf_test.paaverbal + df_rf_test.paamat)/2\n",
    "sns.regplot(df_rf_test.paa_avg, df_rf_test.y_test_hat, x_bins = 15)\n",
    "plt.ylabel(r'$\\^Yprob$')\n",
    "plt.xlabel('PAA Average')\n",
    "plt.show()\n",
    "#plt.savefig(r'C:\\\\Users\\\\Franco\\\\GitHub\\\\teacher-predictions\\\\output\\\\Pr_vs_paa_avg.pdf', bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Graph 1.4: Likelihood vs GPA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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HFwf4h1d02m2ZOhDlC0RleAqpJ1JsFtMD8QIOIACgtf6mUuoPstIqMadCH1oq\n5PbNtl/jlz6xhUjEqKw438f4qhoXj91h9EpOXxzgcPsNum+MTbvu+z8/z8HtDWxaW4F5np7YiC9E\nMByhxGHF5bRiMRdO4F1KMudTXBYTQEaAF5VSX9ZadyYm0qf/LxKigCT3lqQGkC88sG2i5G15IhdX\nIDR/7RK71cLebfXs3VbP9QEfh87e4NDZGxPnz3QNcKZrgJpyx8QKrnKXfdbnS9Yq8QUiOOwWXI70\n9reIwrNShuEW/GuOUmpN4svjQAx4LzH/cR44ppT6uFJKMseJopTMxZVau2Sm0rpTrapx8cht62c8\nNzAa5GeHe/jad4/z3dc6OXdliNgcv1knNygOjAbxDgUyfSkiT1bSMFwmPZC3lVJPaK3/U/KAUmo9\nsB+jpO3/AewB3NlpohD5YdQuMeqXRKLG8FYgNH1vyWz+7ZM7OX7Oy/FzXvzBKLF4nDOXBjhzaWDG\nCfuZRKekagmEolgt5oJZnCCmW0nDcPMGEKVUJfA1rfUziUO/gZGF97e01q8DaK0vA5cxqhMKseyk\nBpPUvSVzpeJyV5fw6O0bePBAE6cv9dPW7qHr+igAg2PBSdeeuzJEc1P1tA2HUw2NhfCHopQk9pUU\n0iIFsfKk89P3Himrq7TWbwMPAX+tlPqNXDVMiEJls5qpcNmpryqhqmz+9Ck2q5lbt9bz24/dwh9+\nZjd37FxFiWPyRpDvvNrJf3vuOL841svI+My1RZJisTjjgQh9wwEGRgL4g5GC+C1XyvquPOkMYT0H\n/CFGzwMArbVWSj0CHFVKfR5ow5gTOa61lhqeYkWYVAgrZuzvmI+7uoRPfWwD997ayJ/945FJ54bG\nQrx2pIc3jvbQvL6a1mY3G1ZVzPl8oUiMUCTEiM9IYV9ityx4t3u2zFbW12w28asPNeelTSK35g0g\nWus/U0q1JB8rpVZjBJRfB36Ekcp9N/Dbib9nXmgvxDJmpE+Z/N9pvl5Jqtt3rOLEuT58iWGxs12D\nnO0apLJ09lVbqeJxowywPxjBYjZNFL5aqiEuKeu7MqX1L6q1bk952AF8Bzigte5KHPtfWW6XEEWv\nvtpJNBrHN0NSx6kePNDEQwebOHNpgLYODxevjgAwPGU4q7NniJb1c8+VRBP1Ssb8YexWs9FLcljm\n3YuyGFLWd2XK5FeCZq31tfkvE2JlM5tMOJxWXE4b4UgUX2J/yWzTFVaLmd1b6ti9pY6+IT9tHR6O\ndnonVUtSxr0cAAAekElEQVT87mudVJbajVxdqp7KeVZzJYe4Rn1knNAxHVLWd2VacP9WgocQC2ez\nWqgsNSbeK1x2bPMMLdVVlfDwbev5D7+8Z9q54fEQbxy9wn/9p+P84ysdtF8enLbcd6pkQseB0SB9\nw358gfCce1EWSsr6rkx5/VdVSj0EfB2wAN/SWn91yvnHgT/F2LAYAf5Qa/1uOvcKUYiSGxVt1vSG\nk6bOYdyxczUnznkZDxg9mY7uITq6h6gotbNf1bO/2U3VPL0SI6FjmFF/GKfdisthmdiJvxhS1nfl\nydsicqWUBfgG8DCwHfisUmr7lMveAHZrrfdgrAL71gLuFaJoVJbasVvn/+/4QOs6vvL5vXz2vq1s\nWVs5cXxkPMTPj/Xy/3zvOP/wcgdnuwbm75UkJt77R7LTK5mtBLHsVVm+8tkDOQCc11pfBFBKPQc8\nDkwUiNZap+bWKuVmEtN57xViqS0mlX2Jw4LNaicSjRmrqUJRYrMEAKvFzM5NtezcVEv/SIAjHR6O\naC/j/jBxQPcMoXuGqHDZ2NfsZr9yU12+0F6JddpKMSGmymcAWQv0pDy+AhycepFS6kngzzFSo3xq\nIfeK4leo9UVmko0qjlaLmXKXnbKSOMFwlJHxueus11Y4efBAE5/c10jH5UEOt3s43zsMwIgvzC+O\n9fLmsV62rqviQIsb1VSNZY4VXKnLgW0Ws7EcOMcruETxKviZLa31C8ALSqm7MeZD7sv0uaqrXViz\nMNY7m/r64l6mWKjt/zf3buHFdy7y2F2bWL2qcsZrFtL2UDg66XFdXXnWViY98+k9PPPp6RPfmbZh\n6nU1Na5Z5yvc9eXcvb8J75Cf905e5f1TVxkZDxHHWP7b2TNEZZmdO3at4fZda6irSm9lVNQEdruV\nEqexaXKq1Pd+se9tLv9tZpPtn/ulfA35/j+bzwDSC6xLedyYODYjrfXbSqlNSqm6hd6bNDjoy7Cp\n86uvL8frHc3Z8+daIbf/4dZ1PNxq/HPP1MaFtj0cmfwfvK9vNCuTyAuRbhumXhcPRRn3hwmFZ69b\nYgHu3rmKO25x03F5iLaOG5zrGSYODI+FeOn9Ll5+v4ut6yppbW6geX1V2vVHLGYTDrsFp83Y8T71\nvV/se7vU/za5+LlfqtewlP9nZwtU+QwgbcBWpdRGjA//p4HPpV6glNoCXNBax5VSezEKWPUDQ/Pd\nK8Ry5LCbKbPaiMZi+INR/MHIrJPlFrOZWzbWcMvGGgZHAxzp8HJEexj1hRO9kmE6e4YpL7GxV9XT\n2uympsI55/ePxuL4EjVLzCawOm0EQ1HsNskQvBLlLYBorSNKqS8DP8P4penbWuszSqlnEuefBZ4C\nfkUpFQb8wC9rrePAjPfm5YUIkSOzJSf84oNqUnbgYCiKLxghOGXoJFV1uZP7W9fxiX2N6O5B2to9\ndPYMEQdG/WHeOnGVt05cZcvaSg60uGnZUD1vryQWN1KYDI4FMZnAYbPMOb8ilp+8zoForV8CXppy\n7NmUr78GfC3de4VYTtJNTuiwW3DYLRO9El8wMusKLovZxPYNNWzfUMOP3r1IW7sHq9VMKGxkzD3f\nO8z53mHKSmzsS+wrqZ2nVwLG5HsgFCU8TxVHsbwU/CS6ECtRJskJLeabvZJAKII/GJ21VxKNxTjS\n4SUWh0gkxufu38pR7aWz2+iVjE3plbS2uGlZX73glWXeoQAVpfYlTewolo4EELHiFMPS4MUmJ0ym\nmY9EY/iC04tfxWI3qx3G4qDWVbNjYy1DY0EjB5f2TtQlSfZKSp1W9ql6WpsbqK2cv1cC0xM7JrME\nF+J7LhZOAohYcbKxXyPXspWc0Goxil+Vl9gIhKL4AhHCcxR4qipzcP/+dXxibyOdPUMcbr9hzJXE\nYTwQ4e2T13j75DU2r62gtdnNHQtIklhItUsAnn/rAq8fvcJ9+xp56p7NeWtHMZMAIlakp+7ZXNAf\nGsnkhG+duDrtXCbJCU0mo0ZIicNKOBKbliZ+KovZRMv6alrWVzM0FuSo9nKkwzNx34XeES70jvCT\n9y9z69Y6Wpvdae8rSd2saDWbcDqslDgsaS8lzoZINMYrh7qJxuK8cqibx+/cWJC/SBQ6CSBCFKhc\nJSe0Wc1UltrSvr6qzMEn9zVy761r6ewZoq3DQ0f3IPG4MVfyzqlrvHPqGpvWVLB3W/2C2hJJGeKy\nmOGH71yadD511Vk2xePxiSG8aCxeECWBi5EEECGW2HzLc5OSyQlTA0iukhPWVjgIR2IEQrNvUDSb\nTTSvr6Z5fTXD4yGOdHg4fq6PgZEAABevjkwUwsrEv755kbYOz6RjUhK3sEmfTYglNtvy3O++1jnL\nHblns5qpLHNQX11CucuGdZ79HJWldj65r5E/e+Z2fvUhZVRJnOGW//lSOyfO9827vNcfjNDRPTjj\nuePnvAzPsqBA5Jf0QIRYQoVeO9xsMlHqtFHqtBEKGzvd5+uVqKZqVFM1I+MhDrd7+PmxKxPnu66P\n0nV9lBKHlb3b6mhtbsBdPX2uZHAkwKhv5sSRI+NhLlwbpsldNrGKaynnS8Ts5F9BiCWUzvLcQmG3\nWYxeSZXRK5lvl3lFqZ179qyZdCx5iz8Y4b2PrvOX/3KSb754hhPnJvdKqiuclLtmnpcpd9moLnMQ\nicYZ9YXxDgUYHA3iD0ayWlVRLJz0QIRYQsVYO9xsvtkrSSdtSqo/+uU9nDzfzxHtYXA0CKT0St63\nsHdrPftb3DRUu2huqp42BwLQ3FRNiWPyR1UwbGySNI0bO/GddgsOm+wvWWoSQIRYQtlenrvUkmlT\nkoWv5qsTUu6yc+/etdxz6xou9A5zuN1De9cgsXgcfzDKe6ev897p66xfVc7+bfVEIjGOpwzx7dtW\nz2N3bJj1+eMYKVQCoSgmEzhtFpx2qyR3XCKF/dMqxDK0HGqHJwtf1dW6CPmD+AIRInOU0DWbTGxt\nrGJrYxWjvhDHOr20tXsYSPRKLl8f5fL1UZz2yRsLH7tzI5Y0V53F4+APRfGHophN4MjDZsV0V9gt\nF8vvFQlR4JZT7XCTyYTLaaOuqoSqsvTqupe77NyzZy1/9PQefv2RZnZsqpnoyQRCk4fGTpzzEoqk\nN1yWKpbYrDgwGsQz5GfEF5pWpyMXCnGFXS5JD0QIkRVOuxVrpXlSnrG5FkvN1ysBeOGdS7x8qJs9\nW+s40NLAqhrXgtsVS6lhYjGbEqu4sj+8Vegr7HKh+H7lEUIUrGSeMbvNzIMHmqgsdaT1YZ3slfz+\np3dNOxcIRfnwzA3++7+e4m9/eJqj2jOtbGy6orE444EI/SPB+S9eoGJaYZctyyscCiHybmqesWR6\neV8gQmieDYVTJ+UfaF3H0U4v/cPGbvcezxg9njF+8v7lRK/Ezera0kW3eWAkSLnLhtNuxZxh76QY\nV9gtlgQQIUTOTUovH4jgD0VIZwvHHTtXc8+eNVy8NkJbu4czlwaIxuIEw1EOnb3BobM3WOcuo7XZ\nza7NtRlPmIciMUZ8YUZ9Yey2xLJgu2XeVWapin2FXSaW3ysSQhQsq8VMRamdMpeNQDAy7+otMCbq\nN6+pZPOaSsb8YY53emnr8NA3pVfy0w+MXklrs5s1dZn1SuJM3mOSDCbp1jBZDivsFkICiBBiyZkT\nq7dcThvBsFGnJJ15jbISG3ftXsOdu1Zz6doIbR0eTl+c3itprC+ltaWBXZtrcWTYK0kNJiMpwWSu\nnslSJsAsBBJAhBB55bAZu8ijsRgj4zPnw5rKZDKxaU0lm9ZU8ujtYY539tHWcQPvkNErueId54r3\nIj/9oIs9W+pobWlgbYa9Epi9Z7LQYa7lRgKIEKIgGDXdF/6RVOq0ceeu1dyxcxVd10dpa/dw+lI/\nkWicUDjG4XYPh9s9rK0rpbXFze7NdRlPlMP0YLKSU6lIABFCFKx06pQkmUwmNq6uYOPqCh4NbOD4\nOS+H2z14h4zls7194/S+c4mXPrjMzk21WWlfaioVs8noTS0mOBWb5TkwJ4SY1WzpNiJz1ErPl4k6\nJVUllDqtM9YcmYnLaeWOnav5w8/s4rcf286tW+uwWoybQ5EYRzu9k66fugM+E7FEKpWpy3iXc8Zg\n6YEIUcBMJtOknd3ZGCKZLd1GIVf+M5tNlLvslJYYq7fGA5GJkrRzMZlMbFhVwYZVFXzqYxs4cd7o\nlXgGJ2/q+2/PHWf35loOtDSwtr40q0NR3sEApSW2ZTlnIgFEiAKW3Nn92pEe7t+/btGreYo93Ubq\n6q10NycmuZxWbt+xmo/dsoqLV0f4/37aPnEuHIlxRHs5or2srnXR2uJmz5Y6nPbFvxczTcCXOJbH\nnEnh/qQIIYDpO7sXI510G03O8qx8r1xLbk4MR2L4AuG05knA6JU0NUx+je7qkoleybV+Hy++28XL\nH3aze3MtrS0NNGapVzIpmCyD9PMSQIRYQZZjuo3kPElZLMZ4III/mN4u91S/98QOrg/4ONzu4aML\n/YSjsem9kmY3e7Zmp1cCM6efd9osRRVMJIAIsYIs53QbFrOZCpedMqcNXzDCeCCcdiBJ9kqaGsr5\n1MfWc/J8H4fbPVwf8AGJXsl7Rq9k1+ZaWlvcrHOXZe2DPpl+3ijSlZ9aJpko3p8WIURGlnu6DbPZ\nRFmJDZfTii8wPZBEozFefPfSpHtefPcST9xlFK8qcVi57ZZVHNzewBXvGIfbPZy60E84EiMcNVZw\nHe30sqrGxf5mN7durZtWcncxJgWTRPr5ErsVWxq1VpaaBBAhVpiVkm7DbJocSHyBMLE4vPhe17Rl\nvEc7vZjNJp68e9PEMZPJxDp3OevcRq/kxLk+2jo8XOs3eiXXB3z85P0uXjl02eiVNDfQ1FCW1deQ\nWsvEajbhdFhx2i0F828lAUQIsaylBpKB4QAd3YMzXtfRPYg/GJmxN+G03+yV9HrHOdzh4dT5PkKR\nGJFonGOdfRzr7MNdXcK+bfU5eR2RWJwxf5gxfxirxYSz1EE0FsMyV9WuHJMAIoQoGLnY95JkNpkY\nDxgp22cy6gszOBacczjKZDLR6C6j0V3GI7c1cfJ8P23tN7ia6JV4Bv28fKh70j3xHGwkjETjjIyH\nGBgKYLeaExmDM69lkqnC6AcJIQSTKxo+dLAp60M1yVVoMyl32aguc6T9XE67lYPbG/jyU7v4vSd3\nsL/ZPWNN+G+8cJr3PrqGLxDJuN1zSdYy8Qz5GRgJ4AtElmz3u/RAhBAFJZv7XqaaaxXaLRtrcDms\nae0lmaqxvozG+jI+ddt6jnV6+fH7XRPnvEN+fvrBZX52uJsdG40VXBtWledkqW4oEiMUCTHqW3gt\nk0zkNYAopR4Cvg5YgG9prb865fznga8AJmAU+F2t9cnEua7EsSgQ0VrvX7qWCyGK1Wyr0L74oMJk\nMnbr+4MR0siUMo3DbmF/s3tSALFbzRNzJSfO93HifB/1VU5amxvYu60Ol9OWhVc12SuHu3n/9HXu\n2LGKBw824bDlJmNw3oawlFIW4BvAw8B24LNKqe1TLrsE3KO13gn8KfDNKefv1VrvkeAhhEhXchVa\nquQqNIvZTLnLTn1VCRUuO9YszCn8x8/eypN3b6Kx/mY9Eu9QgJc+vMyff+cY//zzc1y8OpK1uZJo\nLMa7p64RjsR459Q1IlEjm/HQWAjvkJ/h8RDBNIp3pSOfPZADwHmt9UUApdRzwOPA2eQFWuv3U67/\nEGhc0hYKIVYkk8mEy2nF5bROVEzM9EPXYbPQ2uymtdnN1b5xDrff4OT5foLhKNFYnJPn+zl5vp+6\nSietLW72bqundBG9kliMiUST0VicWAySU0nT9pgkeiaZbljMZwBZC/SkPL4CHJzj+i8BL6c8jgOv\nK6WiwN9praf2ToQQYtGSFRMjUSNVSiAYyWieBGBNXSlP3LWJR25bz6kL/Rxuv8EV7zgAfcMBXv6w\nm1cP93DLxhpaW9xsWl2Rs/mLWCyOLxjBl7Jh0Uilkn4wKYpJdKXUvRgB5M6Uw3dqrXuVUm7gNaVU\nh9b67bmep7rahdWau9QA9fXFkYRuNsXc/mJr+9T633V15UuatiKb37/Y3ntY3OuPxuKM+UKzpkoJ\nRyY/d02NC9sMnzurGip44PaNXLkxyjsnr3LozDUCQaNXcupCP6cu9OOuLuHOPWu5bcdqKkqnrx6r\nqZlepjfd7z/r6zObjESVDsu8eb/yGUB6gXUpjxsTxyZRSu0CvgU8rLXuTx7XWvcm/vYopV7AGBKb\nM4AMDvqy0OyZ1deX4/WO5uz5c62Y21+MbZ/6n7yvb3RB/8kL5fsX43sP2Xn9lpTf4GMpM+7hKenl\nBwZ8c6YhcdnMPLi/kXt3r+aji/0cbvfQ4xkDjH0lP/jFeX701gW2b6jhQIubjWsqMJtM1NSUMjAw\nPsNrW9j3n4vZBC6njY1NNTOez2cAaQO2KqU2YgSOp4HPpV6glGoCfgB8UWvdmXK8FDBrrUcTXz8A\n/MmStVwIseIlc26VOq0EQlHGA2Ei0cwnwu02C/uUm33KzbX+cdraPZw430cgZPRKPrrYz0cX+6mt\ncNLa7OYTB9dn8dXMLBaf3ltLlbcAorWOKKW+DPwMYxnvt7XWZ5RSzyTOPwv8Z6AW+BulFNxcrtsA\nvJA4ZgW+p7V+JQ8vQ4iMpO64tlqyu+NaLC2TyUSJw0qJw5hwHx0PTdpNn0mmkdW1pTx250Yeuq2J\n0xcHONx+g+4bRq+kfyTAK4e7ee1IDy0bqjnQ3MCmtRV5qXSY1zkQrfVLwEtTjj2b8vVvAr85w30X\ngd05b6AQOZJaafDxuzcXTHI8sTgOmwVHVQkPtK7jjaNXuH3HqkXlqrJbLezdVs/ebfVcH/DR1uHh\neKd3oldy+uIApy8OUFPumFjBla16Jekoikl0IZaj5I7rYp1HELP7zL1b+My9W26udEpkAl6MVTUu\n/rfbN/DQgSY+utjPifN9nL8yDMDAaJCfHe7htbYrNK+vysIrSI8EECGEyJFsz5OAUYFx77Z67rtt\nA+0XvLS1ezh+zos/GCUWj3O2a3K24VFfiJoK56K+52wkgAghRI5NnSdZzMbEVA3VLh69fQMPHmji\nzCVjrqTr+uTe7P/7zydoXl/NgZYGtjRWZnWuRAKIEEIsodSNib5ABH9o4TXcp7JZzezZWseerXVc\n7Rvnr3/w0cS5WBzOdg1ytmuQqjI7rc0N7FP1M+4rWSgJIEIIkQdWi5mKUjtlJbYZ95Nkqr6qZNLj\nDavKJ3olQ2MhXjvSwxtHe2heX01rs5utjVUZ1xGRACKEEHmUi3mSVL/+SAtDY0Ha2j0c6/QagWpK\nr2R/s7H/pHKBvRIJIEIIUQAmzZMkAkloyq7yTNVXlfDIx9bzwIF1ibkSD5eujQBGr+T1I1f4+dEr\nqKZqWlvcbEuzVyIBRIgVKJelY8XiOewWHHYL4UjUSOAYSm/CPRqN8eK7lyYde/HdSzxx10YsFjNW\ni5ndW+rYvaWOviE/bR0ejnZ6E1UMof3yIO2XB6ksNXol+1X9tCGxVLJ7SYgVKNelY0V22KwWqsoc\n1FU6cTmtzBfnX3yvi6Od3knHjnZ6efG9rmnX1lWV8PBt6/njz+/l6U9uYdOaiolzw+Mh3jh6hf/6\nT8f59kvts34/6YEIsULlsnSsyC6rxUyFKzHhHjAm3KfyByN0dA/OcDd0dA/iD0YocUz/yLdazOza\nXMeuzXX0Dfs50uHhqPYyHjBWh03dVzLp3sxfkhBCiKVkNt2ccC8rdzAy7JuYcB8cCTDqC89436gv\nzOBYcMYAkqqusoSHDq7nvv3raL88SFu7h/O9w7NeLwFECCGKjFEx0UZdZcnExsTqCiflLtuMQaTc\nZaO6zJH281stZnZuqmXnplrmmkuXgU8hhChiDpuF6nIH69xl7Ng4c92O5qbqeXsfs5lrfkwCiBBC\nLANWi5lff6SFO3eumnR837Z6HrtjQ06+pwQQIYRYJqwWM198UE069sTdm7DkaJWdBBAhxIqT3AcD\nLPt9MPWVDipL7Vgt2X+NEkCEECtOch+Mw25Z9vtgkjvc6ypLqC5zYMvia5VVWEKIFempezbzzKf3\nrKhiXskd7sFwlHH/4lOlSAARQogVJplSPhyJMubPvDaJBBAhhFihbFYL1eUWwpEYvkCYQCjKQvIA\nSwARQogVzmY1U1nmoCyWKHKVSPk+HwkgQgghALCYzZQncm75g1F8gZlToyRJABFCCDGJkSrFistp\nJTzHRPvyXbsmhBBi0WxWSWUihBAiyySACCGEyIgEECGEEBmRACKEECIjEkCEEEJkRAKIEEIsI0uZ\naVgCiBBCLCPJTMN2mznnmYZlI6EQQiwzT92zmafu2Zzz7yM9ECGEEBmRACKEECIjeR3CUko9BHwd\nsADf0lp/dcr5zwNfAUzAKPC7WuuT6dwrhBAit/LWA1FKWYBvAA8D24HPKqW2T7nsEnCP1non8KfA\nNxdwrxBCiBzKZw/kAHBea30RQCn1HPA4cDZ5gdb6/ZTrPwQa071XCCFEbuVzDmQt0JPy+Eri2Gy+\nBLyc4b1CCCGyrCiW8Sql7sUIIHcu5nmqq11YrZbsNGoG9fXlOXvupVDM7S/mtkNxt7+Y2w7F3f58\ntz2fAaQXWJfyuDFxbBKl1C7gW8DDWuv+hdw7ldVqyd2WTCGEWGHyGUDagK1KqY0YH/5PA59LvUAp\n1QT8APii1rpzIfcKIYTIrbzNgWitI8CXgZ8B7cD3tdZnlFLPKKWeSVz2n4Fa4G+UUieUUkfmunfJ\nX4QQQqxgpng8nu82CCGEKEKyE10IIURGJIAIIYTIiAQQIYQQGSmKfSCFSCn1GeD/AlqAA1rrI7Nc\n14WRxysKRLTW+5eoiXNaQPsLLueYUqoG+GdgA9AF/JLWenCG67ookPc+jbxvpsT5RwAf8Gta62NL\n3tBZpNH+jwM/wkg/BPADrfWfLGkjZ6GU+jbwKODRWu+Y4XzBvvdptP3j5PF9lwCSudPAvwH+Lo1r\n79Va9+W4PQs1b/tTco7dj7Hbv00p9aLWOt8pY/4YeENr/VWl1B8nHn9llmvz/t6n+T4+DGxN/DkI\n/G3i77xbwM/BO1rrR5e8gfP7e+CvgX+c5XzBvvfM33bI4/suQ1gZ0lq3a611vtuRqTTbP5FzTGsd\nApI5x/LtceAfEl//A/BEHtuSjnTex8eBf9Rax7XWHwJVSqnVS93QWRTqz0FatNZvAwNzXFKw730a\nbc8rCSC5FwdeV0odVUr9dr4bs0CFmnOsQWt9LfH1daBhlusK5b1P530s1Pca0m/b7UqpU0qpl5VS\ntyxN07KikN/7dOTtfZchrDkopV4HVs1w6j9prX+U5tPcqbXuVUq5gdeUUh2J3ypyLkvtz4u52p76\nQGsdV0rNtpkpb+/9CnQMaNJajymlHgF+iDEkJHIrr++7BJA5aK3vy8Jz9Cb+9iilXsAYDliSD7Es\ntD+jnGPZMFfblVI3lFKrtdbXEkMNnlmeI2/v/RTpvI95e6/TMG/btNYjKV+/pJT6G6VUXb7nn9JU\nyO/9nPL9vssQVg4ppUqVUuXJr4EHMCavi8VEzjGllB0j59iLeW4TGG341cTXv4qxCmWSAnvv03kf\nXwR+RSllUkrdBgynDNPl27ztV0qtSqxmQil1AOOzpX/aMxWmQn7v55Tv9116IBlSSj0J/BVQD/xU\nKXVCa/2gUmoNxjLHRzDG5l9QSoHxXn9Pa/1K3hqdIp32a60jSqlkzjEL8O0CyTn2VeD7SqkvAZeB\nXwIo1Pd+tvcxmfNNa/0s8BLGMtLzGEtJfz0fbZ1Jmu3/NPC7SqkI4Aee1loXRJ4kpdQ/AR8H6pRS\nV4D/Atig8N/7NNqe1/ddcmEJIYTIiAxhCSGEyIgEECGEEBmRACKEECIjEkCEEEJkRAKIEEKIjMgy\nXiFyTCllw9hB/1kgkvhzDqNk8wHgLzGyCtsxSjT/ltZ6IHGvBegGjmitiyb/lFgZpAciRO79T2AX\ncFBrfQuwJ3FMJc6/rrXeA+zAyN/1f6bc+xBwFbhTKTVbzi8h8kICiBA5pJTaCjwJfElrPQRG/i6t\n9U+11i+kXqu1jgE/52ZgAfgN4FngBeBXlqbVQqRHAogQuXUrcG6mgldTKaUcwGPA8cTjOuATwPcx\neiwFs0NaCJA5ECGWlFJqO/A9wAW8jBEs7lNKnUhc8h7w54mvvwj8WGs9CrynlLIqpT6mtf5gqdst\nxEwklYkQOZQYwjoBrE0OYSWOfxnYD7wJPKq1/vQM954C3EAgcagS+Fet9W/lut1CpEOGsITIIa31\nOYxswf9DKVWZcqp0rvuUUq1AFbBaa71Ba70BY5L9M0opV67aK8RCSAARIvd+DejAqCV+Rin1LrAP\n+O9z3PMbwD+lZlZN1Dc5Bnwmh20VIm0yhCWEECIj0gMRQgiREQkgQgghMiIBRAghREYkgAghhMiI\nBBAhhBAZkQAihBAiIxJAhBBCZEQCiBBCiIz8/+7p5rrBctfwAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a71ac668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(df_rf_test.nem, df_rf_test.y_test_hat, x_bins = 15)\n",
    "plt.ylabel(r'$\\^Yprob$')\n",
    "plt.xlabel('GPA')\n",
    "plt.show()\n",
    "#plt.savefig(r'C:\\\\Users\\\\Franco\\\\GitHub\\\\teacher-predictions\\\\output\\\\Pr_vs_gpa.pdf', bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2. Sensitivity Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Graph 1.5: Accuracy of the model by each level likelihood"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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wiXL7MuCjtSWSJA1UleGjDwMfKn8BEBEvAa6tMZckaUAqDR8FiIgnAG8FjgcWAMtqyiRJ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\nCCSp4f4fo+61I/mex1AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a5696160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "accuracy_list = []\n",
    "pr_list = list(np.unique(y_test_hat[:,1][y_test_hat[:,1]>=.5]))\n",
    "for pr in pr_list:\n",
    "    acc = np.mean(y_test[y_test_hat[:,1]>=pr] == y_test_predict[y_test_hat[:,1]>=pr])\n",
    "    accuracy_list.append(acc)\n",
    "\n",
    "ticks = np.arange(len(accuracy_list))\n",
    "pr_list = [round(x, 2) for x in pr_list]\n",
    "ticks_label = [str(x) for x in pr_list]\n",
    "\n",
    "plt.bar(ticks,accuracy_list, align='center', alpha=0.7, color = 'gray')\n",
    "plt.xticks(ticks, ticks_label)\n",
    "plt.xlabel('Y hat')\n",
    "plt.ylabel('Accuracy: 1 - Pr(failure)')\n",
    "plt.show()\n",
    "#plt.savefig(r'D:\\\\Google Drive\\\\Teacher Quality\\\\4. Work\\\\Prediction\\\\Appendix\\\\accuracy.pdf', bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.3. Cross Validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn import tree, svm\n",
    "from sklearn.ensemble import AdaBoostClassifier, AdaBoostRegressor\n",
    "from sklearn.tree import DecisionTreeClassifier, DecisionTreeRegressor\n",
    "#CrossValidation Excercise Accuracy tests:\n",
    "accuracy_type2_rf = []\n",
    "accuracy_overall_rf = []\n",
    "\n",
    "accuracy_type2_dt = []\n",
    "accuracy_overall_dt = []\n",
    "\n",
    "accuracy_type2_svc = []\n",
    "accuracy_overall_svc = []\n",
    "\n",
    "accuracy_type2_lr = []\n",
    "accuracy_overall_lr = []\n",
    "\n",
    "# Cross Validate\n",
    "\n",
    "for i in range(10):\n",
    "\n",
    "    X_train_transformed, X_test_transformed, y_train, y_test = train_test_split(X_transformed, Y, test_size=0.15)\n",
    "\n",
    "    clf = RandomForestClassifier()\n",
    "    clf = clf.fit(X_train_transformed, y_train)\n",
    "    y_test_hat = clf.predict(X_test_transformed)  #Prob of bad Teacher\n",
    "    acc_overall = np.mean(y_test == y_test_hat)\n",
    "    acc_type2 = np.mean(y_test[y_test_hat==1] == y_test_hat[y_test_hat==1])\n",
    "    accuracy_overall_rf.append(acc_overall)\n",
    "    accuracy_type2_rf.append(acc_type2)\n",
    "\n",
    "    clf = DecisionTreeClassifier()\n",
    "    clf = clf.fit(X_train_transformed, y_train)\n",
    "    y_test_hat = clf.predict(X_test_transformed)  #Prob of bad Teacher\n",
    "    acc_overall = np.mean(y_test == y_test_hat)\n",
    "    acc_type2 = np.mean(y_test[y_test_hat==1] == y_test_hat[y_test_hat==1])\n",
    "    accuracy_overall_dt.append(acc_overall)\n",
    "    accuracy_type2_dt.append(acc_type2)\n",
    "\n",
    "    clf = LogisticRegression()\n",
    "    clf = clf.fit(X_train_transformed, y_train)\n",
    "    y_test_hat = clf.predict(X_test_transformed)  #Prob of bad Teacher\n",
    "    acc_overall = np.mean(y_test == y_test_hat)\n",
    "    acc_type2 = np.mean(y_test[y_test_hat==1] == y_test_hat[y_test_hat==1])\n",
    "    accuracy_overall_lr.append(acc_overall)\n",
    "    accuracy_type2_lr.append(acc_type2)\n",
    "    \n",
    "    if (i+1)%50 == 0:\n",
    "        print(f\"Crosvalidation: {i}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Graph 1.6: Cross Validation Random Forest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GT4DffUVPTUmZR15eAf39fdTWVhkUoBAJROIXItaZxL/c1Dh8Pi+NjfXExMSS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\ncZw6wx2/4zhOnfH/3OphGsD00mcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a55989b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.kdeplot(accuracy_overall_rf, alpha=0.8, color = 'orange', label = 'Overall Accuracy')\n",
    "sns.kdeplot(accuracy_type2_rf, alpha=0.8, color = 'gray', label = 'Type 2 Error')\n",
    "plt.xlabel('Prediction success')\n",
    "plt.ylabel('Density')\n",
    "plt.legend(loc=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Graph 1.7: Cross Validation Random Forest vs Decision Tree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ep3Ni5ILP/msh0yTwxyEajaL1V0yYMJGioqIet/X7/VRUDGfDBgn8QvQXbhAP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\nZ8afm5uL3++npaU5rv2i+RPBDMc+cFJ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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a5598208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.kdeplot(accuracy_overall_rf, alpha=0.8, color = 'orange', label = 'Random Forest')\n",
    "sns.kdeplot(accuracy_overall_dt, alpha=0.8, color = 'gray', label = 'Decision Tree')\n",
    "sns.kdeplot(accuracy_overall_lr, alpha=0.8, color = 'black', label = 'Logistic Regression')\n",
    "plt.xlabel('Prediction success')\n",
    "plt.ylabel('Density')\n",
    "plt.legend(loc=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Graph 1.8: Cross Validation RF vs DT (type 2 error)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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lM5rphV9rXZ2mHCLNgsEg7e2tdHd30dfXR39/P/39fbE//QSD/RiGcdg2breb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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a5558940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.kdeplot(accuracy_type2_rf, alpha=0.8, color = 'orange', label = 'Random Forest')\n",
    "sns.kdeplot(accuracy_type2_dt, alpha=0.8, color = 'gray', label = 'Decision Tree')\n",
    "plt.xlabel('Prediction success')\n",
    "plt.ylabel('Density')\n",
    "plt.legend(loc=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.4. Get importance of the variables of the best model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('paaverbal', 0.32753325425906343)\n",
      "('paamat', 0.3224290078151495)\n",
      "('nem', 0.23984579968860748)\n",
      "('took_soc', 0.021307701444666816)\n",
      "('took_hist', 0.019797129839159898)\n",
      "('male', 0.015100565938707889)\n",
      "('took_fis', 0.014660656406235253)\n",
      "('took_mat', 0.014464221208898537)\n",
      "('took_qui', 0.014455818561389019)\n",
      "('took_bio', 0.010405844838122158)\n"
     ]
    }
   ],
   "source": [
    "clf = RandomForestClassifier()\n",
    "clf = clf.fit(X_train_transformed, y_train)\n",
    "y_test_hat = clf.predict(X_test_transformed)  #Prob of bad Teacher\n",
    "acc_overall = np.mean(y_test == y_test_hat)\n",
    "acc_type2 = np.mean(y_test[y_test_hat==1] == y_test_hat[y_test_hat==1])\n",
    "accuracy_overall_rf.append(acc_overall)\n",
    "accuracy_type2_rf.append(acc_type2)\n",
    "\n",
    "importance = clf.feature_importances_\n",
    "FeatImp = {}\n",
    "\n",
    "feature_list = list(X_train_transformed.columns)\n",
    "\n",
    "for x in range(0,len(feature_list)):\n",
    "    if importance[x]>0:\n",
    "        FeatImp[feature_list[x]]=importance[x]\n",
    "        \n",
    "s = [(k, FeatImp[k]) for k in sorted(FeatImp, key=FeatImp.get, reverse=True)]\n",
    "for item in s:\n",
    "    print(item)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Graph 1.9: Contribution of each feature to the prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a54ed358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.bar(range(len(FeatImp)), list(FeatImp.values()), align='center')\n",
    "plt.xticks(range(len(FeatImp)), list(FeatImp.keys()), rotation='vertical')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.4. Prediction of the portfolio score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn import linear_model\n",
    "from sklearn.metrics import r2_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Graph 1.10: Portfolio vs PAA - Math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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bL9pc25Tkruu1TRTdXdSjAsZxXQ4fm2bfkBcw9g9PcPDwJOky83+HQyE29LQx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\nMfw5AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a6ee1550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(X_transformed.paamat, y_pf, x_bins = 15)\n",
    "plt.ylabel(r'Portfolio Score')\n",
    "plt.xlabel('PAA - Mathematics')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Graph 1.11: Portfolio vs PAA - Verbal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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I3ayri4xMyRA7FuPQ+DRLy9fr4FzJkH07exg7NccrOTWpqlkV0H1svAFwb92M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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a6ee1ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(X_transformed.paaverbal, y_pf, x_bins = 15)\n",
    "plt.ylabel(r'Portfolio Score')\n",
    "plt.xlabel('PAA - Verbal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Graph 1.12: Portfolio vs GPA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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CQix4owExHDaxLBvLtqnwZQ6KNQ1L+N2HN+JwGDgMcBgG+nJ/xv3KdKGilOWa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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a6f30828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(X_transformed.nem, y_pf, x_bins = 15)\n",
    "plt.ylabel(r'Portfolio Score')\n",
    "plt.xlabel('GPA')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train_transformed, X_test_transformed, y_train, y_test = train_test_split(X_transformed, y_pf, test_size=0.25)\n",
    "\n",
    "clf = linear_model.LinearRegression()\n",
    "clf.fit(X_train_transformed, y_train)\n",
    "pred_train_lr = clf.predict(X_train_transformed)\n",
    "pred_test_lr = clf.predict(X_test_transformed)\n",
    "ls_r = clf.score(X_test_transformed, y_test)\n",
    "\n",
    "clf = linear_model.RidgeCV()\n",
    "clf.fit(X_train_transformed, y_train)\n",
    "pred_train_rd = clf.predict(X_train_transformed)\n",
    "pred_test_rd = clf.predict(X_test_transformed)\n",
    "clf.score(X_train_transformed, y_train)\n",
    "rcv_r = clf.score(X_test_transformed, y_test)\n",
    "\n",
    "clf = linear_model.Lasso(alpha = 0.1)\n",
    "clf.fit(X_train_transformed, y_train)\n",
    "pred_train_la = clf.predict(X_train_transformed)\n",
    "pred_test_la = clf.predict(X_test_transformed)\n",
    "clf.score(X_train_transformed, y_train)\n",
    "lasso_r = clf.score(X_test_transformed, y_test)\n",
    "\n",
    "clf = linear_model.ElasticNet(alpha = .06)\n",
    "clf.fit(X_train_transformed, y_train)\n",
    "pred_train_en = clf.predict(X_train_transformed)\n",
    "pred_test_en = clf.predict(X_test_transformed)\n",
    "clf.score(X_train_transformed, y_train)\n",
    "enet_r = clf.score(X_test_transformed, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "OLS R2: 0.0164 \n",
      "Ridge R2: 0.0164 \n",
      "Lasso R2:  0.0040 \n",
      "ENet R2:  0.0124\n"
     ]
    }
   ],
   "source": [
    "print(\"OLS R2: %.4f \\nRidge R2: %.4f \\nLasso R2:  %.4f \\nENet R2:  %.4f\" % (ls_r, rcv_r, lasso_r, enet_r))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Graph 1.13: Predicted portfolio (OLS) vs portfolio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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wd+9uKio24nQ6yMjIJD09g4SEhFMby+JQIgT6SyQfKqVeBaqBbGAVgFLKCtiD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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a55d4320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(pred_test_lr, y_test, fit_reg=False, ci=False, x_bins = 15, color='orange', label='OLS fit - test data')\n",
    "plt.plot(np.array(np.linspace(-.3, .3, num=5)), np.array(np.linspace(-.3, .3, num=5)), color='gray',alpha=.8,linestyle='--', label='45 degree line')\n",
    "plt.ylabel(r'Portfolio Score')\n",
    "plt.xlabel('Predicted Portfolio Score')\n",
    "plt.legend()\n",
    "ax = plt.gca()\n",
    "ax.set_ylim([-.3, .3])\n",
    "ax.set_xlim([-.3, .3])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Graph 1.14: Predicted portfolio (Ridge) vs portfolio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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BDkyIwW7Xrp1s27YFl8vFiBFZzJw5m/j4+J7fKMQA6zKRaK0dwGNeXv8M+CyQ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\nCCGEXySRCCGE8Mv/B15psHBcvjmCAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a7205e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(pred_test_rd, y_test, fit_reg=False, ci=False, x_bins = 15, color='orange', label='Ridge - test data')\n",
    "plt.plot(np.array(np.linspace(-.3, .3, num=5)), np.array(np.linspace(-.3, .3, num=5)), color='gray', alpha = .8, linestyle='--', label='45 degree line')\n",
    "plt.ylabel(r'Portfolio Score')\n",
    "plt.xlabel('Predicted Portfolio Score')\n",
    "plt.legend()\n",
    "ax = plt.gca()\n",
    "ax.set_ylim([-.3, .3])\n",
    "ax.set_xlim([-.3, .3])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Graph 1.14: Predicted portfolio (Elastic Net) vs portfolio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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P6wr4VaADEyJS9DcGMtiZ69u3b2Pz5o24XBPJse3kjKS/k+ra45cJi0L4U6+J\nRGttBx7t4fXlwPJABiVEpOh/DOShQc9cb2w8htVqZdasUxg79lo6HN+nTootijDk1TwSIUTPvBoD\nSZ3ZOXM9K6GW+tbMHhOB0+lk//495ORMxGQykZ9fyIwZBcTFxQP9T1gUIlQkkQjhg4GMgRjWNBg2\nBsPReFLb2tpqSkq+4NixBsxmM+PGTcBqtSJl7UQkkEQihA98rd7rcNjZsqWUHTvKAZg0KZeRI6VK\nr4gsXiUSpdR0YKFn82Ot9bbAhSREZBnsGEhV1WFKSr6gubmJ5OQUiovnYbONCEbIQviVNwtbXQcs\nBo6PKP6PUuperfWffD25UupC4Anc81Ke11ov7rbf5Nm/CGgBbtBar/f1vEL41SCr9zY2NtLS0oRS\n08jLy8dikRsEIjJ58y/3bqBIa30YQCmVDbwP+JRIlFIW4GngPOAAsFYp9Y7WemuXZhcBuZ4/84Bn\nPP8VIux4Mxi+b98+rNZkYmKsTJw4mawsm8xMFxGvrxIpnY4nke4/+2guUKG13uWZo/I6cGm3NpcC\nr2itDa31aiBdKTXST+cXImja2lpZvXo57733HmVlpQCYTCZJIiIqeHNFslMp9RDwrGf7v4Bdfjj3\naGB/l+0DnHy10VOb0cCh/g5us0XvasDR3DeIrv4ZhkFFRQUrV66kvb2dESNGUFRUwLBh0dPH7qLp\n8+tJtPdvMLxJJLcATwKlgAF8BHwnkEH5Q3X1yY9YRgObLSVq+wbR1b+WlmbWrfuCw4cPYbFYmDlz\nNqecUkxNTVPU9LG7aPr8ehLN/fMlQXqzQmIVcNWgz9C7SmBsl+0xntcG2kaIsNTS0sLhw4cYMSKb\noqJ5JCUlYzKZQh2WEH7X18JWp2mtVyilFvW0X2vdc10I760FcpVSE3Anh6twL5zV1TvAbUqp13Hf\n9mrQWvd7W0uIUGlsPIbZbCYpKZmsLBtnn30BGRmZkkBEVOvriuQGYAXwgx72GXz5OPCgaK0dSqnb\ncD8BZsG93kmZUuoWz/7fec6xCKjA/fjvjb6cU4hAcblcbN9eTlnZJjIzbZx55jmYTCYyM7NCHZoQ\nAWcyDCPUMQSCEc33MaO1bxCZ/Tt6tJ61a1dx9Gg9cXHxFBbOYcyYnsvDR2L/BkL6F7lstpRBXzb3\ndWtrel9v7DbfQ4io1tOiVU6nk23btlBeXoZhGOTkTGDWrCJiY+NCHK0QwdXXra1/9bHPACb6ORYh\nwk8fi1ZNNKcCAAAaL0lEQVR1dDipqNAkJCRQVDSP7OxRoY5WiJDoaz2SCcEMRIhw1H3RKldbLa27\n3yYZYPrjnH76QtLS0j2VeoUYmgZTtHGp1ro8cCEJER66L1p1oG00n9ctwDBMfC3xA0y5DWRl2UIY\noRDhod8SKZ6ijR8Cszx/PlJKXRPowIQIteOLVrU74/is9kyWVF1MkyOZyUk7iLUfwty6L9QhChEW\nQla0UYhw50rIYae9kFVV02lxJpJpreXMzM/Iiq05adEqIYayUBZtFCKsOS0plDSfQ7srjjlpa/ha\n9ltkxdYA3i1aJcRQEcqijUKEHcMwOHasgbS0dMxmM4XnfIeU3b/E1nQYc4fL60WrhBhKorZooxAD\n1dzcxPr1a6iqOsJ55y0iNTWN9IzhkPEY9fYHBrRolRBDSV8TEu/SWj8G5GqtA1G0UYiwYBgGO3du\nZ/PmjTgcDrKzRxITc+L/Gt4sWiXEUNXXFck1wGPAb4DC4IQjRHAdO9ZASclqamtriI2NZc6cU8jJ\nmSBFFoUYgL4SSatS6p/AeKXUX7rv1FpfGbiwhAiO8vIt1NbWMGbMWGbPnkN8fEKoQxIi4vSVSL6C\nez31fPoulyJERGlubiIpKRmA/PxCRo8ey+jR8iivEIPVV4mUOuANpVS71vrtrvuUUqkBj0wIP3M6\nnWzdWorWWznllAWMHj2W+PgESSJC+Mibp7YeAN7u9tqnyLiJiCA1NVWsXbuapqZGkpKSsFpjQx2S\nEFGjr6e2YoBYwKyUSgCOjz6mAYlBiE0In9ntdrZs2UhFxXYAcnMVeXkFUmRRCD/q64rkh8BPPD83\nd3n9GO6nuYQIe3v27KSiYjupqakUFc2XIotCBEBfYyQPAQ8ppZ7SWt8WxJiE8ElHRzsWSwwWi4VJ\nk6YAJiZOnIzFYgl1aEJEpT5rbSmlLMCpQYpFCJ8dOLCP9957l/LyMgDMZjO5uUqSiBAB1Gci0Vo7\ngSalVHyQ4hFiUFpbW1m58jNWrfocu71DxkCECCJvntrSwDKl1JtAU+eLWv82YFEJ0Y/ja6g748ex\nu7KWTZvWYbfbsdmGU1Q0j5QUeUJdiGDxJpHEAGXAtC6vGYEJR4h+dFtD/ZBrOuuPXIo5ZQKFhXOY\nODFXypsIEWT9JhKt9Y3BCEQIbySX30P8gRexGzFYzDDSvJXTk81kT5iPMUlqiwoRCv0mEqWUCfg2\ncK7npQ+A57XWclUigspkb6C58nM+qPoq8eZWzs/6AJMJZqRswdlQQ739J1LiXYgQ8ObW1iPAbOBF\nz/b1QC5wT6CCEqI7l8vF9s0r2b5/AU7DwqTEnbiwYMEJgKXjMObWfVLqXYgQ8CaRXAAUaq0dAJ5K\nwOuQRCKCpK6ulpKS1TQcrSUlxuCMtPcZn7j3hDayhroQoeNNIjFx4uC6wZflUoQIKLvdzrJlH2G3\nO5gwcQqnxG4g/cjek9rJGupChI43ieR94N9KqZc829cD7/lyUqVUBvAGMB7YA1ypta7vod0LwCVA\nldZ6hi/nFJHF4XAQExOD1Wpl1qw5JCQkMGLESOyuQlpjjM6ntvy1hvrxx4ldCTmSkIQYIG8SyT24\n12j/D8/2W8BzPp73PmCp1nqxUuo+z/a9PbR7CXgKeMXH84kI0dHRwbp1a6iudq+bbrFYGD9+4pcN\nzLE0TX8ck/0h/6yh3u1x4hMSk1kqBAvhjT4TiefKYQLwJ631M34876XAWZ6fX8Zdlv6kRKK1XqaU\nGu/H84owduhQJR98sI6GhkZSU9Noa2vtXICqO3+toZ5cfg8JlS90bls6DnduN01/3OfjCzEU9FVG\n/uu4n9RqBOKUUv+htf7YT+cdobU+5Pn5MDDCT8ftZLOl+PuQYSPa+tbW1sbKlSupqKjAbDYzb94c\nZs2aFfj6WB0NUNvzXdqE2vdISHNBrP9vc0Xb59ed9G/o6a+M/Kla641KqYW4S8p7nUiUUh8B2b0c\nt5PW2lBK+X1OSnV1o78PGRZstpSo6pthGHzyyQfU1tYwbFgGF1xwLk6nlbq6loCf23JsCxltB3ve\n2XaQuv1lOFP9+zhxtH1+3Un/IpcvCbKvROLSWm8E0Fp/opQa0BokWutze9unlDqilBqptT6klBoJ\nVA3k2CLyuVwuzGYzJpOJGTMKqK+vY8qUaWRkpAbtf1RXQg7O2GwsHYdP2iePEwvhvb4SSaxSahpf\nPuob33Vba73Vh/O+g/vpr8We//7Dh2OJCGIYBrt372Tr1lLOPvsCEhOTGD48m+HDe7p4DXAs1jQ6\nbItOGCM5Th4nFsJ7fSWSRGBJt9eObxvARAZvMfAXpdRNwF7gSgCl1Cjc5VcWebZfwz0on6WUOgD8\nRGv9Bx/OK0KoqamRdeu+oKrqCFZrDA0NDSQmJoU2Js9jw/5+nFiIocRkGFFZMsuI5vuYkdY3wzDY\nsaOcLVs24XQ6GTVqNLNnzyUxMfGktqHqn3seiR8eJ+5HJH5+AyH9i1w2W8qgJ5p7M49ECJ+Ulm5g\n+/ZtxMXFUVw8n7Fjc8Ku1Lu/HicWYiiSRCICwjCMzmSRm6vo6Ghn5szZxMfLYptCRJs+l9oVYjDq\n6mr58MMlVFW5n4ZKTExizpxTJIkIEaXkikT4jcPhoKyslB07tmEYUFNTFZKnsbqSGlpCBJ4kEuEX\nVVVHWLduNU1NTSQnJ1NUNJ/hw/1esMB7UkNLiKCRRCJ8Vlm5j5UrP8dkgilTppGXl09MTGj/aUkN\nLSGCRxKJGLTjA+rZ2aMZPXosU6fmkZGRGeqwMNkbiK3uPgXKLbZ6CSb7Q3KbSwg/ksF2MWBtbW2s\nXr2cHTvKAbBYLJx66oKwSCIA5ta9PZY9gS+X5BVC+I9ckQivGYbB/v172LChhI6ODtrb28jNnRp2\nc0KkhpYQwSWJRHilpaWZ9evXcOjQQSwWCwUFhWGZREBqaAkRbJJIRL+am5v44IN/4XA4GD48m6Ki\nuSQnh/eaDFJDS4jgkUQi+pWYmMTo0WOx2YYzfvyksLwKOYm/l+QVQvRKEok4icvlYvv2clpamigs\nnIvJZGLu3FNDHdagSA0tIQJPEok4wdGj9ZSUrKa+vo64uHjy8vKJi5PSJkKI3kkiEQA4nU62bdtC\neXkZhmGQkzOegoJi4uLiQh2aECLMSSIRuFwuPv74PY4ePUpCQiJFRfMYOXJUqMMSQkQISSQCs9nM\nqFFjycy0MXPmbKxWa6hDEkJEEEkkQ9SRI4fYtWsH8+adjtlsZvr0mZHxNJYQIuxIIhliOjo6KC1d\nz+7dOzGZoLa2GptthCQRIcSgSSIZQior97N+/Rra2tpIT0+nqGh+2NTHAnexReoqMNltMudDiAgi\niWSI2LChhIoKjdlsZsaMApSajtkcJjU7u6wdQsdhhsnaIUJEFEkkQ8Tw4SOor6+luHg+qanh9du+\nrB0iRGQLk19Jhb+1tDSzevVy2traABg9eiwLF54fdkmk/7VDGoIckRBioOSKJMoYhsGuXTsoLd2A\nw+EgPX0YU6fmAYTlgLo3a4dIiRMhwpskkijS2HiMkpLV1NRUY7VamTNnPjk5E0MdVp9k7RAhIp8k\nkiixb98e1q5dhcvlYvToMcyePZeEhIRQh9UvWTtEiMgniSRKpKcPIz4+noKCIsaMiazf4mXtECEi\nW0gSiVIqA3gDGA/sAa7UWtd3azMWeAUYARjAc1rrJ4IbafhyF1nczKhRY8nIyCQ1NY2LLro0fB7p\nHYgua4dkJdRS35opVyJCRJBQfevcByzVWucCSz3b3TmAu7TW04H5wH8rpaYHMcawVVNTzYcfLmHb\ntjK2bt3c+Xook4jJ3oDlWKlPT1kZ1jQYViBJRIgIE6pbW5cCZ3l+fhn4FLi3awOt9SHgkOfnRqXU\nNmA0sDVoUYYZu93OihUr2LTJnTwmT57CjBmzQhtUl8mEJ92WksmEQgwJoUokIzyJAuAw7ttXvVJK\njQdmA18EOK6w1dBQz/Lln9HR0UpKSgrFxaeQlWULdVgymVAIEbhEopT6CMjuYdcPu25orQ2llNHH\ncZKBvwF3aK2PeXt+my3F26YRIS0tjri4GPLyZlNYWIjFYgl1SNDRALXv9bgrofY9EtJcEDvw21TR\n9tl1J/2LbNHev8EwGUav3+EBo5TSwFla60NKqZHAp1pr1UM7K/Au8L7W+lcDOIVRXd3op2hD58CB\nfRiGwdixOQA4nQ6ys4cRLn2zHCsl44vTe91fN28FztSBTSa02VLCpn+BIP2LbNHcP5stZdAzlkN1\na+sd4Hpgsee//+jeQCllAv4AbBtgEol4bW2trF+/lsrK/cTHxzNq1BgsFgsWS3g9rS2TCYUQELpE\nshj4i1LqJmAvcCWAUmoU8LzWehFwGnAdsFkptdHzvvu11j0XZooChmGwd+8uNm1aT0dHB1lZNoqL\n54fHbaweyGRCIQSEKJForWuBc3p4/SCwyPPzciD8ikMFiN3ewapVn3PkyGFiYmKYPXsOkyblhmV9\nrK5kMqEQIrzulQxhMTFWXC4X2dkjKSycS1JScqhD8k6XyYTm1n24EsbJlYgQQ4wkkhA6dqyBqqoj\nTJ48BZPJxGmnnUVMTEzYX4X0xLCmSZVeIYYoSSQh4HK50HorW7duxuVyMWJENikpqVit1lCHJoQQ\nAyaJJMjq6+soKVnF0aNHiY+Pp7BwLikpqaEOSwghBk0SSZAYhkFZ2SbKy8swDJgwYRL5+bOJjY0L\ndWhCCOETSSRBYjKZcDgcJCYmUVQ0jxEjRoY6JCGE8AtJJAFkt9vZvbuC3NypmEwmZsyYxYwZBcTE\nyFiIECJ6SCIJkEOHDrJu3Re0trYQFxdHTs5EYmLkr1sIEX3km83P2tvb2bSphL1792AymZg2bQZj\nxuSEOiwhhAgYSSR+VFm5n3Xr1tDe3sawYRkUF88nPX1YqMMSQoiAkkTiR3Z7B3Z7BzNnzmbKlKmR\nueytEEIMkCQSHxiGwb59uxk1aixWq5WcnIkMH55NYmJSqEMTQoigkUQySE1Njaxbt4aqqsNMnlzH\n7NnFmEwmSSJCiCFHEskAGYbBjh3lbNmyCafTSXb2KJSaFuqwhBAiZCSRDMCxYw2UlKymtraG2NhY\niormMW7c+IgssiiEEP4iiWQAHA4HdXU1jB2bw6xZRcTHJ4Q6JCGECDlJJP2oq6vFarWSkpJKRkYm\n559/Campst6GEEIcJ4mkF06ng7KyUrZv30ZGRhYLF56PyWSSJCKEEN1IIulBdfURSkpW09TURFJS\nMnl5BTIOIoQQvZBE0oXdbqe0dAO7du3AZIIpU6aSl1cgNbKEEKIP8g3ZhdPppLJyH6mpaRQXzycz\nMyvUIQkhRNgb8omkvb2NpqYmMjOziI+PZ8GCc0hJScVisYQ6NCGEiAhDNpEYhsH+/XvZuLEEk8nE\nBRdcQmxsnBRZFEKIARqSiaSlpYUNG9Zw8GAlFouFvLx8WWxKCCEGaUglEsMw2L27gtLS9djtDmy2\n4RQVzSclJSXUoQkhRMQacolk584dABQVzWXChMnyWK8QQvgo6hOJYRjU1taQlWXDbDYzf/7pWCwx\nJCYmhjo0IYSIClGdSBoajlJSspqjR+s499yLSEsbRkpKaqjDEkKIqBKSRKKUygDeAMYDe4Artdb1\n3drEA8uAONxxvqm1/ok3x3c6nZSVlVJevgWXy2DcuPFSYFEIIQIkVGvB3gcs1VrnAks92921A2dr\nrQuAWcCFSqn53hz8rbfeYuvWzcTFxXPaaWcyb95pxMXF+y14IYQQXwrVra1LgbM8P78MfArc27WB\n1toAmjybVs8fw5uD19XVMXHiZPLzZ2O1xvojXiGEEL0wGYZX381+pZQ6qrVO9/xsAuqPb3drZwHW\nAZOBp7XW93ZvI4QQIrQCdkWilPoIyO5h1w+7bmitDaVUj9lMa+0EZiml0oG3lFIztNZb/B+tEEKI\nwQpYItFan9vbPqXUEaXUSK31IaXUSKCqn2MdVUp9AlwISCIRQogwEqrB9neA6z0/Xw/8o3sDpZTN\ncyWCUioBOA8oD1qEQgghvBKqRLIYOE8ptQM417ONUmqUUmqJp81I4BOlVCmwFvhQa/1uSKIVQgjR\nq5AMtgshhIgeoboiEUIIESUkkQghhPBJxNfaCnS5lVDzsn9jgVeAEbgnbT6ntX4iuJEOjjf987R7\nAbgEqNJazwhmjIOhlLoQeAKwAM9rrRd322/y7F8EtAA3aK3XBz3QQfCib1OBF4FC4Ida60eDH+Xg\nedG/a3BPoDYBjcCtWutNQQ90kLzo36XATwEX4ADu0Fov7+uY0XBFEtByK2HAm/45gLu01tOB+cB/\nK6WmBzFGX3jTP4CXcD/+HfY8E2mfBi4CpgPf6OHzuAjI9fz5NvBMUIMcJC/7VgfcDkRUAgGv+7cb\nOFNrPRP3F+5zwY1y8Lzs31KgQGs9C/gW8Hx/x42GRHIp7jIreP57WfcGWmtDaz2ocithwJv+HTr+\n26zWuhHYBowOWoS+6bd/AFrrZbi/oCLBXKBCa71La90BvI67n11dCrzi+be5Gkj3zKkKd/32TWtd\npbVeC9hDEaCPvOnfyi5XzauBMUGO0Rfe9K/JU6IKIAkvvisj/tYWMEJrfcjz82Hct3dO0kO5lS+C\nFJ+vvOrfcUqp8cBsICr7FyFGA/u7bB8A5nnRZjRwiPDmTd8i2UD7dxPw74BG5F9e9U8p9TXgF8Bw\n4OL+DhoRiSTay634o3+e4yQDf8N9T/OYf6McPH/1T4hwopRaiDuRnB7qWPxNa/0W7u/JBbhv3/Va\nqQQiJJFEe7kVf/RPKWXFnUT+pLX+e4BCHRR/fn4RohIY22V7jOe1gbYJR5Eat7e86p9SKh/32MFF\nWuvaIMXmDwP6/LTWy5RSE5VSWVrrmt7aRcMYSbSXW/GmfybgD8A2rfWvghibP/Tbvwi0FshVSk1Q\nSsUCV+HuZ1fvAN9USpk8D340dLnFF8686Vsk67d/SqlxwN+B67TW20MQoy+86d9kz3cKSqlC3E+7\n9pksoyGRRHu5FW/6dxpwHXC2Umqj58+i0IQ7YN70D6XUa8Aq94/qgFLqppBE6wWttQO4DXgf94MP\nf9FalymlblFK3eJptgTYBVQAvwf+X0iCHSBv+qaUylZKHQDuBH7k+bwiYo1rLz+7B4BM4Lee/9dK\nQhTugHnZv/8EtiilNuJ+wuvrXQbfeyQlUoQQQvgkGq5IhBBChJAkEiGEED6RRCKEEMInkkiEEEL4\nRBKJEEIIn0TEhEQRuZRSe4A23IUzLcDPtNav++m4l2itt3geE/6u1npnH+0vAw5qrdcM4lw3eM51\neQ/7PgXGAceAeOCZwVReVkrdAfxZa13l2Y4F3sY9YWyp1vr7fbz3U+BRrfW7Sqn/Bcq01m8M4Nwm\n4CHcj306cNeiez4C5ySJEJErEhEMl3sqL18HvKiUyurewFMLbVC01ov6SiIel+EuWBcIt3sqpZ4H\n/K9SqsDbNyqlzJ4v8jtw1zU6bjaQo7XO7yuJdKe1fmAgScTjcuBsoMjzOc0G3hvgMXrly2crIoNc\nkYig0VpvUEo1AhOUUpcA1+JezyEXuFYpdQT4De7f8BOA17TWPwdQSp0B/NZzqM9wrwWBZ98evrw6\nGQ086TkmwGvAeuCrwLlKqZuBX2mtX1FKXY97ImAM0IB7XQntuRr4De4v1xpgg5f926+U0sAUYJNS\n6l7cyRPcE2G/q7VuUko9COQBaZ6+vgqMAt5USrXhnuH/J2CUZ1LYL4B/eWKa4zneK1rrR7rHoJR6\nCSjRWj/lqb3W73twX/XU4L5qRGvdDmztcsxvAd/zbHbg/rs+opT6JvAD3NVhdwLf0VpXea7gvP5s\nReSTKxIRNJ4id/HADs9L84G7tdYztNYbcS/O9aTWei5QBFyklDpPKRWHu9z1dz1rQCzD/YXUkz8C\nqz2/yecDv9dav4+7DMRirfUsTxI5A7gSWKC1LgL+D3jBc4zvABNwr9dwDl5eyXjWdZgKlCqlLsKd\nRE4FZuK+rffjLs3nAVdrradqrR8GDuK+cpvlWSTpZmCrZ/sNz3vNnmOdClzvOUdfvH3P68A0YIdS\n6kWl1LVKqRhPn84C7gcu8FytLAQalFIzcFchON/z97wFd6I4zqvPtp/4RYSQRCKC4U3Pb9YPAf+p\ntT7qeX358VtSSqkk4CzgSU/bNbh/S58GKKBFa/0pgNb6L7ivIE7g+Q38VODXx1/ro9DcV4AC4AvP\n+RbzZTG7hcDLWmu71roFd3Lqy/GYX8D9W7nGXe7lda31MU95iec4sYLqkr6K4PXgXNxJ0fBUdn6N\nfiqyevseT42vPOBGYDvuqszHSwhdjPtK5rCnbZPWug3339GSLvXBnu12bG8/WxEF5NaWCIbLeynZ\n39TlZzPuWyRztNYnLIjkqbTana+1fUzAC1rrB3w8DrjHSAZau62p/ybB46nB9DnwuXIva3xYuZdB\nHiyvPlsRHeSKRIQF7V7Z8XO6LLWrlBqrlMoGNJDguR2FUupyIL2HYzQBK4HvdznG8YH9Y7jHJI77\nJ+7qu2M87SxKqSLPvo+B65RSMZ5q0VcPoksfAV9XSqV4BtNvBj7so333+Ho63k2easEpuKu29nU8\nr9+jlCpS7gXRjisE6oGjuMdmvqmUGuFpm6yUigc+ARZ5Ph+A/+otnn4+WxEF5IpEhJNrgF8rpTZ7\nthuBb2mtDyulvoG72qqBe4xkXy/HuBZ42jOQ7gT+DPwS94D2S0qpK/hysP2HwDuep4pigb/iXkXz\nOSAfd3XUGtwD5QNauVFr/W/PldQqz0slwM/6eMuTuJ9oa6HnxPVT4Cng+N/Nq1rr/p6s8vY9Wbj/\nblNxD7i3AJdprV3Ap0qpXwAfKaVcnv1f8TzYcB/woecz2YV7bKk3PX62uFfFFBFOqv8KIYTwidza\nEkII4RNJJEIIIXwiiUQIIYRPJJEIIYTwiSQSIYQQPpFEIoQQwieSSIQQQvjk/wOAa9W/mF2bEAAA\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a71fb518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(pred_test_en, y_test, fit_reg=False, ci=False, x_bins = 15, color='orange', label='Ridge - test data')\n",
    "plt.plot(np.array(np.linspace(-.3, .3, num=5)), np.array(np.linspace(-.3, .3, num=5)), color='gray', alpha = .8, linestyle='--', label='45 degree line')\n",
    "plt.ylabel(r'Portfolio Score')\n",
    "plt.xlabel('Predicted Portfolio Score')\n",
    "plt.legend()\n",
    "ax = plt.gca()\n",
    "ax.set_ylim([-.3, .3])\n",
    "ax.set_xlim([-.3, .3])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.5. Prediction of the Portfolio Score without GPA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train_transformed2 = X_train_transformed.drop(['nem'], axis = 1)\n",
    "X_test_transformed2  = X_test_transformed.drop(['nem'], axis = 1)\n",
    "\n",
    "clf = linear_model.LinearRegression()\n",
    "clf.fit(X_train_transformed2, y_train)\n",
    "pred_train_lr_2 = clf.predict(X_train_transformed2)\n",
    "pred_test_lr_2 = clf.predict(X_test_transformed2)\n",
    "ls_r_2 = clf.score(X_test_transformed2, y_test)\n",
    "\n",
    "clf = linear_model.RidgeCV()\n",
    "clf.fit(X_train_transformed2, y_train)\n",
    "pred_train_rd_2 = clf.predict(X_train_transformed2)\n",
    "pred_test_rd_2 = clf.predict(X_test_transformed2)\n",
    "clf.score(X_train_transformed2, y_train)\n",
    "rcv_r_2 = clf.score(X_test_transformed2, y_test)\n",
    "\n",
    "clf = linear_model.Lasso(alpha = 0.1)\n",
    "clf.fit(X_train_transformed2, y_train)\n",
    "pred_train_la_2 = clf.predict(X_train_transformed2)\n",
    "pred_test_la_2 = clf.predict(X_test_transformed2)\n",
    "clf.score(X_train_transformed2, y_train)\n",
    "lasso_r_2 = clf.score(X_test_transformed2, y_test)\n",
    "\n",
    "clf = linear_model.ElasticNet(alpha = .06)\n",
    "clf.fit(X_train_transformed2, y_train)\n",
    "pred_train_en_2 = clf.predict(X_train_transformed2)\n",
    "pred_test_en_2 = clf.predict(X_test_transformed2)\n",
    "clf.score(X_train_transformed2, y_train)\n",
    "enet_r_2 = clf.score(X_test_transformed2, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "OLS R2: 0.0059 \n",
      "Ridge R2: 0.0059 \n",
      "Lasso R2:  -0.0000 \n",
      "ENet R2:  0.0001\n"
     ]
    }
   ],
   "source": [
    "print(\"OLS R2: %.4f \\nRidge R2: %.4f \\nLasso R2:  %.4f \\nENet R2:  %.4f\" % (ls_r_2, rcv_r_2, lasso_r_2, enet_r_2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Graph 1.15: Predicted portfolio (OLS) vs portfolio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PpENh4aQBP9aSMvKRV0Y+MzOTpUuX8cc/eu4elJrG8uU38K//+s+Ap7Pd12OtBx/8Dk8+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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a6fa5c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(pred_test_lr, y_test, fit_reg=False, ci=False, x_bins = 15, color='orange', label='OLS fit - test data')\n",
    "sns.regplot(pred_test_lr_2, y_test, fit_reg=False, ci=False, x_bins = 15,  color='gray', label='OLS fit - test data - No GPA')\n",
    "plt.plot(np.array(np.linspace(-.3, .3, num=5)), np.array(np.linspace(-.3, .3, num=5)), color='gray',alpha=.8,linestyle='--')\n",
    "plt.ylabel(r'Portfolio Score')\n",
    "plt.xlabel('Predicted Portfolio Score')\n",
    "plt.legend()\n",
    "ax = plt.gca()\n",
    "ax.set_ylim([-.3, .3])\n",
    "ax.set_xlim([-.3, .3])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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vgWpzf8nH05+Uv/Zy7OGBThJCmOhMAi9LKVcc+LqUsklK2dL19QeASQgR72FM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\nHMdpcjwQOI7jNDkeCBzHcZqc/wdTlIBfREjs9gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a55d4400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.kdeplot(pred_test_lr, color='orange', label='OLS fit - test data')\n",
    "sns.kdeplot(pred_test_lr_2, color='gray', label='OLS fit - test data - No GPA')\n",
    "plt.ylabel(r'Density')\n",
    "plt.xlabel('Predicted Portfolio Score')\n",
    "plt.legend()\n",
    "ax = plt.gca()\n",
    "ax.set_ylim([0, 4.5])\n",
    "ax.set_xlim([-.6, .5])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Predict probability of work as teacher:\n",
    "This part of the jupyter's notebook computes different models to predict if a student, given their characteristics is going to be a teacher in the future. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>proceso</th>\n",
       "      <th>sit</th>\n",
       "      <th>nem</th>\n",
       "      <th>paa_verbal</th>\n",
       "      <th>paa_matematica</th>\n",
       "      <th>pce_hria_y_geografia</th>\n",
       "      <th>pce_biologia</th>\n",
       "      <th>pce_cs_sociales</th>\n",
       "      <th>pce_fisica</th>\n",
       "      <th>pce_matematica</th>\n",
       "      <th>pce_quimica</th>\n",
       "      <th>region</th>\n",
       "      <th>male</th>\n",
       "      <th>privado</th>\n",
       "      <th>tFLcode_app</th>\n",
       "      <th>fl_teacher</th>\n",
       "      <th>isteacher</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1981</td>\n",
       "      <td>24</td>\n",
       "      <td>720</td>\n",
       "      <td>670</td>\n",
       "      <td>553</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>644</td>\n",
       "      <td>0</td>\n",
       "      <td>517</td>\n",
       "      <td>574</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>74</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1981</td>\n",
       "      <td>24</td>\n",
       "      <td>603</td>\n",
       "      <td>670</td>\n",
       "      <td>609</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>551</td>\n",
       "      <td>608</td>\n",
       "      <td>13.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>47</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   proceso  sit  nem  paa_verbal  paa_matematica  pce_hria_y_geografia  \\\n",
       "0     1981   24  720         670             553                     0   \n",
       "1     1981   24  603         670             609                     0   \n",
       "\n",
       "   pce_biologia  pce_cs_sociales  pce_fisica  pce_matematica  pce_quimica  \\\n",
       "0             0              644           0             517          574   \n",
       "1             0                0           0             551          608   \n",
       "\n",
       "   region  male  privado  tFLcode_app  fl_teacher  isteacher  \n",
       "0     5.0   0.0      0.0           74           1          0  \n",
       "1    13.0   1.0      0.0           47           0          0  "
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_path = os.getcwd() + '/data/proceso_evdoc.csv'\n",
    "df = None\n",
    "#with open(df_path, encoding=\"utf-16\") as f:\n",
    "with open(df_path, \"r\") as f:\n",
    "    df = pd.read_csv(f)\n",
    "\n",
    "df.head(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "tests = ['pce_fisica', 'pce_quimica', 'pce_biologia', 'pce_matematica', 'pce_cs_sociales', 'pce_hria_y_geografia']\n",
    "for test in tests:\n",
    "    df['took_'+str(test)] = (df[test]==0)\n",
    "\n",
    "\n",
    "scores = ['nem', 'paa_verbal', 'paa_matematica', 'pce_fisica', 'pce_quimica', 'pce_biologia', 'pce_matematica', 'pce_cs_sociales', 'pce_hria_y_geografia']\n",
    "df[scores] = (df[scores] - df[scores].mean())/df[scores].std()\n",
    "\n",
    "df.head(1)\n",
    "vars = ['proceso', 'nem', 'paa_verbal', 'paa_matematica', 'pce_fisica', 'pce_quimica', 'pce_biologia', 'pce_matematica', 'pce_cs_sociales', 'pce_hria_y_geografia', 'took_pce_fisica', 'took_pce_quimica', 'took_pce_biologia', 'took_pce_matematica', 'took_pce_cs_sociales', 'took_pce_hria_y_geografia', 'fl_teacher', 'isteacher']\n",
    "indepvars = vars[:-2]\n",
    "depvar = vars[-2]\n",
    "depvar2 = vars[-1]\n",
    "\n",
    "teacher_2 = 1   #Activate this when we want to predict if the student is a prefesor given that his/her fl is 1\n",
    "if teacher_2 == 1:\n",
    "    df = df[vars][df['fl_teacher']==1].dropna()\n",
    "    Y = df[depvar2]\n",
    "else:\n",
    "    df = df[vars].dropna()\n",
    "    Y = df[depvar]\n",
    "\n",
    "X = df[indepvars]\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, Y, test_size=0.15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.1. Likelihood of being teacher vs undergrad performance scatterplot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df_rf_test , y_test_hat, y_test_predict = gen_predictions(RandomForestClassifier, X_train, X_test, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_test.mean()\n",
    "y_test_predict.mean()\n",
    "#Accuracy tests:\n",
    "accuracy = np.mean(y_test_predict == y_test)\n",
    "type1_error = np.mean(y_test[y_test==1] == y_test_predict[y_test==1]) #Type 1 error: Probabilidad acierto cuando es profesor\n",
    "type2_error = np.mean(y_test[y_test_predict == 1] == y_test_predict[y_test_predict == 1]) #probabilidad de predecir que es profesor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overall Accuracy: 0.59 \n",
      "Type 1 error: 0.29 \n",
      "Type 2 error:  0.49\n"
     ]
    }
   ],
   "source": [
    "print(\"Overall Accuracy: %.2f \\nType 1 error: %.2f \\nType 2 error:  %.2f\" % (accuracy, type1_error, type2_error))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Graph 2.1: Likelihood vs PAA Math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Xt7x+hC2vH6GmwsPsaVW8s/8MsRhsfft4vwWg4UisX9LsDURwOh0jkmCGK5eV/Rue388z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\n5X8B6yyXuk8bhUAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a5587ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(df_rf_test.paa_matematica, df_rf_test.y_test_hat, x_bins = 25, order =2)\n",
    "plt.ylabel(r'$\\^Yprob$')\n",
    "plt.xlabel('PAA Math')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Graph 2.2: Likelihood vs PAA Verbal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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afJDgcCTDme8IhqJ09AzRHwxL5/g4G0sAOZB8vtb6m8AFYy5Rlcq1vOzeI2fw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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a5688e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(df_rf_test.paa_verbal, df_rf_test.y_test_hat, order =2 , x_bins = 25)\n",
    "plt.ylabel(r'$\\^Yprob$')\n",
    "plt.xlabel('PAA Verbal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Graph 2.3: Likelihood vs GPA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Bx2m3UVLkosiT+Z+m7rFRhWQ8v21XjDGfEZEtwFrgQ+D5iRmWUoVnpBxfff4Q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\nMfn/ARuYyL8i3OT7AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a506f588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(df_rf_test.nem, df_rf_test.y_test_hat, x_bins = 15)\n",
    "plt.ylabel(r'$\\^Yprob$')\n",
    "plt.xlabel('GPA Score')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 2.2. Sensitivity Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "#### Graph 2.4: Accuracy of the model by each level likelihood"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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HgKQzgR2BW6vW8aeq+a8DJhYVtJmZWT1lJ9Wf5X+DtT6wsGp4ETCtwbwAewF/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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a568a588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "accuracy_list = []\n",
    "pr_list = list(np.unique(y_test_hat[:,1][y_test_hat[:,1]>=.5]))\n",
    "for pr in pr_list:\n",
    "    acc = np.mean(y_test[y_test_hat[:,1]>=pr] == y_test_predict[y_test_hat[:,1]>=pr])\n",
    "    accuracy_list.append(acc)\n",
    "\n",
    "ticks = np.arange(len(accuracy_list))\n",
    "pr_list = [round(x, 2) for x in pr_list]\n",
    "ticks_label = [str(x) for x in pr_list]\n",
    "\n",
    "plt.bar(ticks,accuracy_list, align='center', alpha=0.7, color = 'gray')\n",
    "plt.xticks(ticks, ticks_label)\n",
    "plt.xlabel('Y hat')\n",
    "plt.ylabel('Accuracy: 1 - Pr(failure)')\n",
    "plt.title('Likelihood of success when predicting that a student will become a teacher')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 2.3. Cross Validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "accuracy_type2_rf = []\n",
    "accuracy_overall_rf = []\n",
    "\n",
    "accuracy_type2_dt = []\n",
    "accuracy_overall_dt = []\n",
    "\n",
    "accuracy_type2_lr = []\n",
    "accuracy_overall_lr = []\n",
    "\n",
    "for i in range(15):\n",
    "\n",
    "    X_train, X_test, y_train, y_test = train_test_split(X, Y, test_size=0.15)\n",
    "\n",
    "    clf = RandomForestClassifier()\n",
    "    clf = clf.fit(X_train, y_train)\n",
    "    y_test_hat = clf.predict(X_test)  #Prob of being teacher\n",
    "    acc_overall = np.mean(y_test == y_test_hat)\n",
    "    acc_type2 = np.mean(y_test[y_test_hat==1] == y_test_hat[y_test_hat==1])\n",
    "    accuracy_overall_rf.append(acc_overall)\n",
    "    accuracy_type2_rf.append(acc_type2)\n",
    "\n",
    "    clf = DecisionTreeClassifier()\n",
    "    clf = clf.fit(X_train, y_train)\n",
    "    y_test_hat = clf.predict(X_test)  #Prob of being Teacher\n",
    "    acc_overall = np.mean(y_test == y_test_hat)\n",
    "    acc_type2 = np.mean(y_test[y_test_hat==1] == y_test_hat[y_test_hat==1])\n",
    "    accuracy_overall_dt.append(acc_overall)\n",
    "    accuracy_type2_dt.append(acc_type2)\n",
    "\n",
    "    clf = LogisticRegression()\n",
    "    clf = clf.fit(X_train, y_train)\n",
    "    y_test_hat = clf.predict(X_test)  #Prob of being Teacher\n",
    "    acc_overall = np.mean(y_test == y_test_hat)\n",
    "    acc_type2 = np.mean(y_test[y_test_hat==1] == y_test_hat[y_test_hat==1])\n",
    "    accuracy_overall_lr.append(acc_overall)\n",
    "    accuracy_type2_lr.append(acc_type2)\n",
    "\n",
    "    if (i+1)%50 == 0:\n",
    "        print(f\"Crossvalidation: {i}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Graph 2.5: Cross Validation LR vs RF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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+c2NYY/1+P8uXf88555xnnCuJxx9/ktTUNMrLy/ntb6cyYcKJABQU7OShhx7j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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a7004320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.kdeplot(accuracy_overall_lr, alpha=0.8, color = 'orange', label = 'Logistic Regression')\n",
    "sns.kdeplot(accuracy_overall_dt, alpha=0.8, color = 'gray', label = 'Decision Tree')\n",
    "sns.kdeplot(accuracy_overall_rf, alpha=0.8, color = 'black', label = 'Random Forest')\n",
    "plt.xlabel('Prediction success')\n",
    "plt.ylabel('Density')\n",
    "plt.title('Cross validation: Accuracy of Random Forest')\n",
    "plt.legend(loc=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Graph 2.5: Overall Accuracy and Type 2 error of RF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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+c2NYY/1+P8uXf88555xnnCuJxx9/ktTUNMrLy/ntb6cyYcKJABQU7OShhx7j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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a54af828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.kdeplot(accuracy_overall_lr, alpha=0.8, color = 'orange', label = 'Logistic Regression')\n",
    "sns.kdeplot(accuracy_overall_dt, alpha=0.8, color = 'gray', label = 'Decision Tree')\n",
    "sns.kdeplot(accuracy_overall_rf, alpha=0.8, color = 'black', label = 'Random Forest')\n",
    "plt.xlabel('Prediction success')\n",
    "plt.ylabel('Density')\n",
    "plt.title('Cross validation: Accuracy of Random Forest')\n",
    "plt.legend(loc=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Graph 2.5: Overall Accuracy and Type 2 error of RF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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P5Jln/sq//vUKHR0dbN26hc997gvE43Gee+4Z3G4PP/7xPVRXj8hK+5IlS7j99h+QTCaZ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\niRbbgx5Z67SaQaOMvxdSqRStrS2MGFG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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a54df240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.kdeplot(accuracy_type2_rf, alpha=0.8, color = 'orange', label = 'Random Forest')\n",
    "sns.kdeplot(accuracy_type2_dt, alpha=0.8, color = 'gray', label = 'Decision Tree')\n",
    "plt.xlabel('Prediction success')\n",
    "plt.ylabel('Density')\n",
    "plt.title('Cross validation: Accuracy of Random Forest')\n",
    "plt.legend(loc=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
